{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "nbsphinx": "hidden"
   },
   "source": [
    "# Quantization of Signals\n",
    "\n",
    "*This jupyter notebook is part of a [collection of notebooks](../index.ipynb) on various topics of Digital Signal Processing. Please direct questions and suggestions to [Sascha.Spors@uni-rostock.de](mailto:Sascha.Spors@uni-rostock.de).*"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Introduction\n",
    "\n",
    "[Digital signal processors](https://en.wikipedia.org/wiki/Digital_signal_processor) and general purpose processors can only perform arithmetic operations within a limited number range. So far we considered discrete signals with continuous amplitude values. These cannot be handled by processors in a straightforward manner. [Quantization](https://en.wikipedia.org/wiki/Quantization_%28signal_processing%29) is the process of mapping a continuous amplitude to a countable set of amplitude values. This refers also to the *requantization* of a signal from a large set of countable amplitude values to a smaller set. Scalar quantization is an instantaneous and memoryless operation. It can be applied to the continuous amplitude signal, also referred to as *analog signal* or to the (time-)discrete signal. The quantized discrete signal is termed as *digital signal*. The connections between the different domains are illustrated in the following.\n",
    "\n",
    "![Interrelations between analog, discrete and digital signals](analog_discrete_digital.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Model of the Quantization Process\n",
    "\n",
    "In order to discuss the effects of quantizing a continuous amplitude signal, a mathematical model of the quantization process is required. We restrict our considerations to a discrete real-valued signal $x[k]$. The following mapping is used in order to quantize the continuous amplitude signal $x[k]$\n",
    "\n",
    "\\begin{equation}\n",
    "x_Q[k] = g( \\; \\lfloor \\, f(x[k]) \\, \\rfloor \\; )\n",
    "\\end{equation}\n",
    "\n",
    "where $g(\\cdot)$ and $f(\\cdot)$ denote real-valued mapping functions, and $\\lfloor \\cdot \\rfloor$ a rounding operation. The quantization process can be split into two stages\n",
    "\n",
    "1. **Forward quantization**\n",
    "    The mapping $f(x[k])$ maps the signal $x[k]$ such that it is suitable for the rounding operation. This may be a scaling of the signal or a non-linear mapping. The result of the rounding operation is an integer number $\\lfloor \\, f(x[k]) \\, \\rfloor \\in \\mathbb{Z}$, which is termed as *quantization index*.\n",
    "    \n",
    "2. **Inverse quantization**\n",
    "    The mapping $g(\\cdot)$, maps the quantization index to the quantized value $x_Q[k]$ such that it constitutes an approximation of $x[k]$. This may be a simple scaling or non-linear operation.\n",
    "\n",
    "The quantization error (quantization noise) $e[k]$ is defined as\n",
    "\n",
    "\\begin{equation}\n",
    "e[k] = x_Q[k] - x[k]\n",
    "\\end{equation}\n",
    "\n",
    "Rearranging yields that the quantization process can be modeled by adding the quantization error to the discrete signal\n",
    "\n",
    "![Model of the quantization process](model_quantization.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Example - Quantization of a sine signal\n",
    "\n",
    "In order to illustrate the introduced model, the quantization of one period of a sine signal is considered\n",
    "\n",
    "\\begin{equation}\n",
    "x[k] = \\sin[\\Omega_0 k]\n",
    "\\end{equation}\n",
    "\n",
    "using \n",
    "\n",
    "\\begin{align}\n",
    "f(x[k]) &= 3 \\cdot x[k] \\\\\n",
    "i &= \\lfloor \\, f(x[k]) \\, \\rfloor \\\\\n",
    "g(i) &= \\frac{1}{3} \\cdot i\n",
    "\\end{align}\n",
    "\n",
    "where $\\lfloor \\cdot \\rfloor$ denotes the [nearest integer function](https://en.wikipedia.org/wiki/Nearest_integer_function) and $i$ the quantization index. The quantized signal is then given as\n",
    "\n",
    "\\begin{equation}\n",
    "x_Q[k] = \\frac{1}{3} \\cdot \\lfloor \\, 3 \\cdot \\sin[\\Omega_0 k] \\, \\rfloor\n",
    "\\end{equation}\n",
    "\n",
    "The discrete signals are not shown by stem plots for ease of illustration."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/pdf": "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\n",
      "image/svg+xml": [
       "<?xml version=\"1.0\" encoding=\"utf-8\" standalone=\"no\"?>\n",
       "<!DOCTYPE svg PUBLIC \"-//W3C//DTD SVG 1.1//EN\"\n",
       "  \"http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd\">\n",
       "<!-- Created with matplotlib (https://matplotlib.org/) -->\n",
       "<svg height=\"266.51625pt\" version=\"1.1\" viewBox=\"0 0 653.303125 266.51625\" width=\"653.303125pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\">\n",
       " <defs>\n",
       "  <style type=\"text/css\">\n",
       "*{stroke-linecap:butt;stroke-linejoin:round;}\n",
       "  </style>\n",
       " </defs>\n",
       " <g id=\"figure_1\">\n",
       "  <g id=\"patch_1\">\n",
       "   <path d=\"M 0 266.51625 \n",
       "L 653.303125 266.51625 \n",
       "L 653.303125 0 \n",
       "L 0 0 \n",
       "z\n",
       "\" style=\"fill:#ffffff;\"/>\n",
       "  </g>\n",
       "  <g id=\"axes_1\">\n",
       "   <g id=\"patch_2\">\n",
       "    <path d=\"M 52.682813 228.96 \n",
       "L 610.682812 228.96 \n",
       "L 610.682812 7.2 \n",
       "L 52.682813 7.2 \n",
       "z\n",
       "\" style=\"fill:#ffffff;\"/>\n",
       "   </g>\n",
       "   <g id=\"matplotlib.axis_1\">\n",
       "    <g id=\"xtick_1\">\n",
       "     <g id=\"line2d_1\">\n",
       "      <defs>\n",
       "       <path d=\"M 0 0 \n",
       "L 0 3.5 \n",
       "\" id=\"mbb16c0e5ae\" style=\"stroke:#000000;stroke-width:0.8;\"/>\n",
       "      </defs>\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"52.682813\" xlink:href=\"#mbb16c0e5ae\" y=\"228.96\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_1\">\n",
       "      <!-- 0 -->\n",
       "      <defs>\n",
       "       <path d=\"M 31.78125 66.40625 \n",
       "Q 24.171875 66.40625 20.328125 58.90625 \n",
       "Q 16.5 51.421875 16.5 36.375 \n",
       "Q 16.5 21.390625 20.328125 13.890625 \n",
       "Q 24.171875 6.390625 31.78125 6.390625 \n",
       "Q 39.453125 6.390625 43.28125 13.890625 \n",
       "Q 47.125 21.390625 47.125 36.375 \n",
       "Q 47.125 51.421875 43.28125 58.90625 \n",
       "Q 39.453125 66.40625 31.78125 66.40625 \n",
       "z\n",
       "M 31.78125 74.21875 \n",
       "Q 44.046875 74.21875 50.515625 64.515625 \n",
       "Q 56.984375 54.828125 56.984375 36.375 \n",
       "Q 56.984375 17.96875 50.515625 8.265625 \n",
       "Q 44.046875 -1.421875 31.78125 -1.421875 \n",
       "Q 19.53125 -1.421875 13.0625 8.265625 \n",
       "Q 6.59375 17.96875 6.59375 36.375 \n",
       "Q 6.59375 54.828125 13.0625 64.515625 \n",
       "Q 19.53125 74.21875 31.78125 74.21875 \n",
       "z\n",
       "\" id=\"DejaVuSans-48\"/>\n",
       "      </defs>\n",
       "      <g transform=\"translate(49.501563 243.558437)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-48\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_2\">\n",
       "     <g id=\"line2d_2\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"161.667188\" xlink:href=\"#mbb16c0e5ae\" y=\"228.96\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_2\">\n",
       "      <!-- 200 -->\n",
       "      <defs>\n",
       "       <path d=\"M 19.1875 8.296875 \n",
       "L 53.609375 8.296875 \n",
       "L 53.609375 0 \n",
       "L 7.328125 0 \n",
       "L 7.328125 8.296875 \n",
       "Q 12.9375 14.109375 22.625 23.890625 \n",
       "Q 32.328125 33.6875 34.8125 36.53125 \n",
       "Q 39.546875 41.84375 41.421875 45.53125 \n",
       "Q 43.3125 49.21875 43.3125 52.78125 \n",
       "Q 43.3125 58.59375 39.234375 62.25 \n",
       "Q 35.15625 65.921875 28.609375 65.921875 \n",
       "Q 23.96875 65.921875 18.8125 64.3125 \n",
       "Q 13.671875 62.703125 7.8125 59.421875 \n",
       "L 7.8125 69.390625 \n",
       "Q 13.765625 71.78125 18.9375 73 \n",
       "Q 24.125 74.21875 28.421875 74.21875 \n",
       "Q 39.75 74.21875 46.484375 68.546875 \n",
       "Q 53.21875 62.890625 53.21875 53.421875 \n",
       "Q 53.21875 48.921875 51.53125 44.890625 \n",
       "Q 49.859375 40.875 45.40625 35.40625 \n",
       "Q 44.1875 33.984375 37.640625 27.21875 \n",
       "Q 31.109375 20.453125 19.1875 8.296875 \n",
       "z\n",
       "\" id=\"DejaVuSans-50\"/>\n",
       "      </defs>\n",
       "      <g transform=\"translate(152.123438 243.558437)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-50\"/>\n",
       "       <use x=\"63.623047\" xlink:href=\"#DejaVuSans-48\"/>\n",
       "       <use x=\"127.246094\" xlink:href=\"#DejaVuSans-48\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_3\">\n",
       "     <g id=\"line2d_3\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"270.651563\" xlink:href=\"#mbb16c0e5ae\" y=\"228.96\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_3\">\n",
       "      <!-- 400 -->\n",
       "      <defs>\n",
       "       <path d=\"M 37.796875 64.3125 \n",
       "L 12.890625 25.390625 \n",
       "L 37.796875 25.390625 \n",
       "z\n",
       "M 35.203125 72.90625 \n",
       "L 47.609375 72.90625 \n",
       "L 47.609375 25.390625 \n",
       "L 58.015625 25.390625 \n",
       "L 58.015625 17.1875 \n",
       "L 47.609375 17.1875 \n",
       "L 47.609375 0 \n",
       "L 37.796875 0 \n",
       "L 37.796875 17.1875 \n",
       "L 4.890625 17.1875 \n",
       "L 4.890625 26.703125 \n",
       "z\n",
       "\" id=\"DejaVuSans-52\"/>\n",
       "      </defs>\n",
       "      <g transform=\"translate(261.107813 243.558437)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-52\"/>\n",
       "       <use x=\"63.623047\" xlink:href=\"#DejaVuSans-48\"/>\n",
       "       <use x=\"127.246094\" xlink:href=\"#DejaVuSans-48\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_4\">\n",
       "     <g id=\"line2d_4\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"379.635938\" xlink:href=\"#mbb16c0e5ae\" y=\"228.96\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_4\">\n",
       "      <!-- 600 -->\n",
       "      <defs>\n",
       "       <path d=\"M 33.015625 40.375 \n",
       "Q 26.375 40.375 22.484375 35.828125 \n",
       "Q 18.609375 31.296875 18.609375 23.390625 \n",
       "Q 18.609375 15.53125 22.484375 10.953125 \n",
       "Q 26.375 6.390625 33.015625 6.390625 \n",
       "Q 39.65625 6.390625 43.53125 10.953125 \n",
       "Q 47.40625 15.53125 47.40625 23.390625 \n",
       "Q 47.40625 31.296875 43.53125 35.828125 \n",
       "Q 39.65625 40.375 33.015625 40.375 \n",
       "z\n",
       "M 52.59375 71.296875 \n",
       "L 52.59375 62.3125 \n",
       "Q 48.875 64.0625 45.09375 64.984375 \n",
       "Q 41.3125 65.921875 37.59375 65.921875 \n",
       "Q 27.828125 65.921875 22.671875 59.328125 \n",
       "Q 17.53125 52.734375 16.796875 39.40625 \n",
       "Q 19.671875 43.65625 24.015625 45.921875 \n",
       "Q 28.375 48.1875 33.59375 48.1875 \n",
       "Q 44.578125 48.1875 50.953125 41.515625 \n",
       "Q 57.328125 34.859375 57.328125 23.390625 \n",
       "Q 57.328125 12.15625 50.6875 5.359375 \n",
       "Q 44.046875 -1.421875 33.015625 -1.421875 \n",
       "Q 20.359375 -1.421875 13.671875 8.265625 \n",
       "Q 6.984375 17.96875 6.984375 36.375 \n",
       "Q 6.984375 53.65625 15.1875 63.9375 \n",
       "Q 23.390625 74.21875 37.203125 74.21875 \n",
       "Q 40.921875 74.21875 44.703125 73.484375 \n",
       "Q 48.484375 72.75 52.59375 71.296875 \n",
       "z\n",
       "\" id=\"DejaVuSans-54\"/>\n",
       "      </defs>\n",
       "      <g transform=\"translate(370.092188 243.558437)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-54\"/>\n",
       "       <use x=\"63.623047\" xlink:href=\"#DejaVuSans-48\"/>\n",
       "       <use x=\"127.246094\" xlink:href=\"#DejaVuSans-48\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_5\">\n",
       "     <g id=\"line2d_5\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"488.620313\" xlink:href=\"#mbb16c0e5ae\" y=\"228.96\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_5\">\n",
       "      <!-- 800 -->\n",
       "      <defs>\n",
       "       <path d=\"M 31.78125 34.625 \n",
       "Q 24.75 34.625 20.71875 30.859375 \n",
       "Q 16.703125 27.09375 16.703125 20.515625 \n",
       "Q 16.703125 13.921875 20.71875 10.15625 \n",
       "Q 24.75 6.390625 31.78125 6.390625 \n",
       "Q 38.8125 6.390625 42.859375 10.171875 \n",
       "Q 46.921875 13.96875 46.921875 20.515625 \n",
       "Q 46.921875 27.09375 42.890625 30.859375 \n",
       "Q 38.875 34.625 31.78125 34.625 \n",
       "z\n",
       "M 21.921875 38.8125 \n",
       "Q 15.578125 40.375 12.03125 44.71875 \n",
       "Q 8.5 49.078125 8.5 55.328125 \n",
       "Q 8.5 64.0625 14.71875 69.140625 \n",
       "Q 20.953125 74.21875 31.78125 74.21875 \n",
       "Q 42.671875 74.21875 48.875 69.140625 \n",
       "Q 55.078125 64.0625 55.078125 55.328125 \n",
       "Q 55.078125 49.078125 51.53125 44.71875 \n",
       "Q 48 40.375 41.703125 38.8125 \n",
       "Q 48.828125 37.15625 52.796875 32.3125 \n",
       "Q 56.78125 27.484375 56.78125 20.515625 \n",
       "Q 56.78125 9.90625 50.3125 4.234375 \n",
       "Q 43.84375 -1.421875 31.78125 -1.421875 \n",
       "Q 19.734375 -1.421875 13.25 4.234375 \n",
       "Q 6.78125 9.90625 6.78125 20.515625 \n",
       "Q 6.78125 27.484375 10.78125 32.3125 \n",
       "Q 14.796875 37.15625 21.921875 38.8125 \n",
       "z\n",
       "M 18.3125 54.390625 \n",
       "Q 18.3125 48.734375 21.84375 45.5625 \n",
       "Q 25.390625 42.390625 31.78125 42.390625 \n",
       "Q 38.140625 42.390625 41.71875 45.5625 \n",
       "Q 45.3125 48.734375 45.3125 54.390625 \n",
       "Q 45.3125 60.0625 41.71875 63.234375 \n",
       "Q 38.140625 66.40625 31.78125 66.40625 \n",
       "Q 25.390625 66.40625 21.84375 63.234375 \n",
       "Q 18.3125 60.0625 18.3125 54.390625 \n",
       "z\n",
       "\" id=\"DejaVuSans-56\"/>\n",
       "      </defs>\n",
       "      <g transform=\"translate(479.076563 243.558437)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-56\"/>\n",
       "       <use x=\"63.623047\" xlink:href=\"#DejaVuSans-48\"/>\n",
       "       <use x=\"127.246094\" xlink:href=\"#DejaVuSans-48\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_6\">\n",
       "     <g id=\"line2d_6\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"597.604687\" xlink:href=\"#mbb16c0e5ae\" y=\"228.96\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_6\">\n",
       "      <!-- 1000 -->\n",
       "      <defs>\n",
       "       <path d=\"M 12.40625 8.296875 \n",
       "L 28.515625 8.296875 \n",
       "L 28.515625 63.921875 \n",
       "L 10.984375 60.40625 \n",
       "L 10.984375 69.390625 \n",
       "L 28.421875 72.90625 \n",
       "L 38.28125 72.90625 \n",
       "L 38.28125 8.296875 \n",
       "L 54.390625 8.296875 \n",
       "L 54.390625 0 \n",
       "L 12.40625 0 \n",
       "z\n",
       "\" id=\"DejaVuSans-49\"/>\n",
       "      </defs>\n",
       "      <g transform=\"translate(584.879687 243.558437)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-49\"/>\n",
       "       <use x=\"63.623047\" xlink:href=\"#DejaVuSans-48\"/>\n",
       "       <use x=\"127.246094\" xlink:href=\"#DejaVuSans-48\"/>\n",
       "       <use x=\"190.869141\" xlink:href=\"#DejaVuSans-48\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"text_7\">\n",
       "     <!-- k -->\n",
       "     <defs>\n",
       "      <path d=\"M 9.078125 75.984375 \n",
       "L 18.109375 75.984375 \n",
       "L 18.109375 31.109375 \n",
       "L 44.921875 54.6875 \n",
       "L 56.390625 54.6875 \n",
       "L 27.390625 29.109375 \n",
       "L 57.625 0 \n",
       "L 45.90625 0 \n",
       "L 18.109375 26.703125 \n",
       "L 18.109375 0 \n",
       "L 9.078125 0 \n",
       "z\n",
       "\" id=\"DejaVuSans-107\"/>\n",
       "     </defs>\n",
       "     <g transform=\"translate(328.7875 257.236562)scale(0.1 -0.1)\">\n",
       "      <use xlink:href=\"#DejaVuSans-107\"/>\n",
       "     </g>\n",
       "    </g>\n",
       "   </g>\n",
       "   <g id=\"matplotlib.axis_2\">\n",
       "    <g id=\"ytick_1\">\n",
       "     <g id=\"line2d_7\">\n",
       "      <defs>\n",
       "       <path d=\"M 0 0 \n",
       "L -3.5 0 \n",
       "\" id=\"m40c90a4045\" style=\"stroke:#000000;stroke-width:0.8;\"/>\n",
       "      </defs>\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"52.682813\" xlink:href=\"#m40c90a4045\" y=\"210.48\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_8\">\n",
       "      <!-- −1.0 -->\n",
       "      <defs>\n",
       "       <path d=\"M 10.59375 35.5 \n",
       "L 73.1875 35.5 \n",
       "L 73.1875 27.203125 \n",
       "L 10.59375 27.203125 \n",
       "z\n",
       "\" id=\"DejaVuSans-8722\"/>\n",
       "       <path d=\"M 10.6875 12.40625 \n",
       "L 21 12.40625 \n",
       "L 21 0 \n",
       "L 10.6875 0 \n",
       "z\n",
       "\" id=\"DejaVuSans-46\"/>\n",
       "      </defs>\n",
       "      <g transform=\"translate(21.4 214.279219)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-8722\"/>\n",
       "       <use x=\"83.789062\" xlink:href=\"#DejaVuSans-49\"/>\n",
       "       <use x=\"147.412109\" xlink:href=\"#DejaVuSans-46\"/>\n",
       "       <use x=\"179.199219\" xlink:href=\"#DejaVuSans-48\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"ytick_2\">\n",
       "     <g id=\"line2d_8\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"52.682813\" xlink:href=\"#m40c90a4045\" y=\"164.28\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_9\">\n",
       "      <!-- −0.5 -->\n",
       "      <defs>\n",
       "       <path d=\"M 10.796875 72.90625 \n",
       "L 49.515625 72.90625 \n",
       "L 49.515625 64.59375 \n",
       "L 19.828125 64.59375 \n",
       "L 19.828125 46.734375 \n",
       "Q 21.96875 47.46875 24.109375 47.828125 \n",
       "Q 26.265625 48.1875 28.421875 48.1875 \n",
       "Q 40.625 48.1875 47.75 41.5 \n",
       "Q 54.890625 34.8125 54.890625 23.390625 \n",
       "Q 54.890625 11.625 47.5625 5.09375 \n",
       "Q 40.234375 -1.421875 26.90625 -1.421875 \n",
       "Q 22.3125 -1.421875 17.546875 -0.640625 \n",
       "Q 12.796875 0.140625 7.71875 1.703125 \n",
       "L 7.71875 11.625 \n",
       "Q 12.109375 9.234375 16.796875 8.0625 \n",
       "Q 21.484375 6.890625 26.703125 6.890625 \n",
       "Q 35.15625 6.890625 40.078125 11.328125 \n",
       "Q 45.015625 15.765625 45.015625 23.390625 \n",
       "Q 45.015625 31 40.078125 35.4375 \n",
       "Q 35.15625 39.890625 26.703125 39.890625 \n",
       "Q 22.75 39.890625 18.8125 39.015625 \n",
       "Q 14.890625 38.140625 10.796875 36.28125 \n",
       "z\n",
       "\" id=\"DejaVuSans-53\"/>\n",
       "      </defs>\n",
       "      <g transform=\"translate(21.4 168.079219)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-8722\"/>\n",
       "       <use x=\"83.789062\" xlink:href=\"#DejaVuSans-48\"/>\n",
       "       <use x=\"147.412109\" xlink:href=\"#DejaVuSans-46\"/>\n",
       "       <use x=\"179.199219\" xlink:href=\"#DejaVuSans-53\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"ytick_3\">\n",
       "     <g id=\"line2d_9\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"52.682813\" xlink:href=\"#m40c90a4045\" y=\"118.08\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_10\">\n",
       "      <!-- 0.0 -->\n",
       "      <g transform=\"translate(29.779688 121.879219)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-48\"/>\n",
       "       <use x=\"63.623047\" xlink:href=\"#DejaVuSans-46\"/>\n",
       "       <use x=\"95.410156\" xlink:href=\"#DejaVuSans-48\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"ytick_4\">\n",
       "     <g id=\"line2d_10\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"52.682813\" xlink:href=\"#m40c90a4045\" y=\"71.88\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_11\">\n",
       "      <!-- 0.5 -->\n",
       "      <g transform=\"translate(29.779688 75.679219)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-48\"/>\n",
       "       <use x=\"63.623047\" xlink:href=\"#DejaVuSans-46\"/>\n",
       "       <use x=\"95.410156\" xlink:href=\"#DejaVuSans-53\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"ytick_5\">\n",
       "     <g id=\"line2d_11\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"52.682813\" xlink:href=\"#m40c90a4045\" y=\"25.68\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_12\">\n",
       "      <!-- 1.0 -->\n",
       "      <g transform=\"translate(29.779688 29.479219)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-49\"/>\n",
       "       <use x=\"63.623047\" xlink:href=\"#DejaVuSans-46\"/>\n",
       "       <use x=\"95.410156\" xlink:href=\"#DejaVuSans-48\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"text_13\">\n",
       "     <!-- $x[k]$, $x_Q[k]$, $e[k]$ -->\n",
       "     <defs>\n",
       "      <path d=\"M 60.015625 54.6875 \n",
       "L 34.90625 27.875 \n",
       "L 50.296875 0 \n",
       "L 39.984375 0 \n",
       "L 28.421875 21.6875 \n",
       "L 8.296875 0 \n",
       "L -2.59375 0 \n",
       "L 24.3125 28.8125 \n",
       "L 10.015625 54.6875 \n",
       "L 20.3125 54.6875 \n",
       "L 30.8125 34.90625 \n",
       "L 49.125 54.6875 \n",
       "z\n",
       "\" id=\"DejaVuSans-Oblique-120\"/>\n",
       "      <path d=\"M 8.59375 75.984375 \n",
       "L 29.296875 75.984375 \n",
       "L 29.296875 69 \n",
       "L 17.578125 69 \n",
       "L 17.578125 -6.203125 \n",
       "L 29.296875 -6.203125 \n",
       "L 29.296875 -13.1875 \n",
       "L 8.59375 -13.1875 \n",
       "z\n",
       "\" id=\"DejaVuSans-91\"/>\n",
       "      <path d=\"M 18.3125 75.984375 \n",
       "L 27.296875 75.984375 \n",
       "L 18.703125 31.6875 \n",
       "L 49.515625 54.6875 \n",
       "L 61.1875 54.6875 \n",
       "L 26.8125 28.515625 \n",
       "L 51.90625 0 \n",
       "L 41.015625 0 \n",
       "L 17.671875 26.703125 \n",
       "L 12.5 0 \n",
       "L 3.515625 0 \n",
       "z\n",
       "\" id=\"DejaVuSans-Oblique-107\"/>\n",
       "      <path d=\"M 30.421875 75.984375 \n",
       "L 30.421875 -13.1875 \n",
       "L 9.71875 -13.1875 \n",
       "L 9.71875 -6.203125 \n",
       "L 21.390625 -6.203125 \n",
       "L 21.390625 69 \n",
       "L 9.71875 69 \n",
       "L 9.71875 75.984375 \n",
       "z\n",
       "\" id=\"DejaVuSans-93\"/>\n",
       "      <path d=\"M 11.71875 12.40625 \n",
       "L 22.015625 12.40625 \n",
       "L 22.015625 4 \n",
       "L 14.015625 -11.625 \n",
       "L 7.71875 -11.625 \n",
       "L 11.71875 4 \n",
       "z\n",
       "\" id=\"DejaVuSans-44\"/>\n",
       "      <path id=\"DejaVuSans-32\"/>\n",
       "      <path d=\"M 36.078125 -1.3125 \n",
       "Q 35.546875 -1.375 34.953125 -1.390625 \n",
       "Q 34.375 -1.421875 33.203125 -1.421875 \n",
       "Q 19.53125 -1.421875 11.8125 6.421875 \n",
       "Q 4.109375 14.265625 4.109375 28.078125 \n",
       "Q 4.109375 36.234375 7.0625 44.4375 \n",
       "Q 10.015625 52.640625 15.28125 59.1875 \n",
       "Q 21.390625 66.703125 29.03125 70.453125 \n",
       "Q 36.671875 74.21875 45.90625 74.21875 \n",
       "Q 59.28125 74.21875 66.984375 66.328125 \n",
       "Q 74.703125 58.453125 74.703125 44.828125 \n",
       "Q 74.703125 30.125 66.640625 17.921875 \n",
       "Q 58.59375 5.71875 45.609375 0.6875 \n",
       "L 55.515625 -12.890625 \n",
       "L 44.484375 -12.890625 \n",
       "z\n",
       "M 45.609375 66.21875 \n",
       "Q 37.5 66.21875 31.296875 62.28125 \n",
       "Q 25.09375 58.34375 20.515625 50.296875 \n",
       "Q 17.578125 45.171875 16.03125 39.40625 \n",
       "Q 14.5 33.640625 14.5 27.78125 \n",
       "Q 14.5 17.625 19.359375 12.109375 \n",
       "Q 24.21875 6.59375 33.109375 6.59375 \n",
       "Q 41.109375 6.59375 47.375 10.5625 \n",
       "Q 53.65625 14.546875 58.109375 22.40625 \n",
       "Q 61.078125 27.6875 62.640625 33.46875 \n",
       "Q 64.203125 39.265625 64.203125 45.015625 \n",
       "Q 64.203125 55.125 59.3125 60.671875 \n",
       "Q 54.4375 66.21875 45.609375 66.21875 \n",
       "z\n",
       "\" id=\"DejaVuSans-Oblique-81\"/>\n",
       "      <path d=\"M 48.09375 32.234375 \n",
       "Q 48.25 33.015625 48.3125 33.84375 \n",
       "Q 48.390625 34.671875 48.390625 35.5 \n",
       "Q 48.390625 41.453125 44.890625 44.921875 \n",
       "Q 41.40625 48.390625 35.40625 48.390625 \n",
       "Q 28.71875 48.390625 23.578125 44.15625 \n",
       "Q 18.453125 39.9375 15.828125 32.171875 \n",
       "z\n",
       "M 55.90625 25.203125 \n",
       "L 14.109375 25.203125 \n",
       "Q 13.8125 23.34375 13.71875 22.265625 \n",
       "Q 13.625 21.1875 13.625 20.40625 \n",
       "Q 13.625 13.625 17.796875 9.90625 \n",
       "Q 21.96875 6.203125 29.59375 6.203125 \n",
       "Q 35.453125 6.203125 40.671875 7.515625 \n",
       "Q 45.90625 8.84375 50.390625 11.375 \n",
       "L 48.6875 2.484375 \n",
       "Q 43.84375 0.53125 38.6875 -0.4375 \n",
       "Q 33.546875 -1.421875 28.21875 -1.421875 \n",
       "Q 16.84375 -1.421875 10.71875 4.015625 \n",
       "Q 4.59375 9.46875 4.59375 19.484375 \n",
       "Q 4.59375 28.03125 7.640625 35.375 \n",
       "Q 10.6875 42.71875 16.609375 48.484375 \n",
       "Q 20.40625 52.09375 25.65625 54.046875 \n",
       "Q 30.90625 56 36.8125 56 \n",
       "Q 46.09375 56 51.578125 50.4375 \n",
       "Q 57.078125 44.875 57.078125 35.5 \n",
       "Q 57.078125 33.25 56.78125 30.6875 \n",
       "Q 56.5 28.125 55.90625 25.203125 \n",
       "z\n",
       "\" id=\"DejaVuSans-Oblique-101\"/>\n",
       "     </defs>\n",
       "     <g transform=\"translate(14.8 156.73)rotate(-90)scale(0.1 -0.1)\">\n",
       "      <use transform=\"translate(0 0.015625)\" xlink:href=\"#DejaVuSans-Oblique-120\"/>\n",
       "      <use transform=\"translate(59.179688 0.015625)\" xlink:href=\"#DejaVuSans-91\"/>\n",
       "      <use transform=\"translate(98.193359 0.015625)\" xlink:href=\"#DejaVuSans-Oblique-107\"/>\n",
       "      <use transform=\"translate(156.103516 0.015625)\" xlink:href=\"#DejaVuSans-93\"/>\n",
       "      <use transform=\"translate(195.117188 0.015625)\" xlink:href=\"#DejaVuSans-44\"/>\n",
       "      <use transform=\"translate(226.904297 0.015625)\" xlink:href=\"#DejaVuSans-32\"/>\n",
       "      <use transform=\"translate(258.691406 0.015625)\" xlink:href=\"#DejaVuSans-Oblique-120\"/>\n",
       "      <use transform=\"translate(317.871094 -16.390625)scale(0.7)\" xlink:href=\"#DejaVuSans-Oblique-81\"/>\n",
       "      <use transform=\"translate(375.703125 0.015625)\" xlink:href=\"#DejaVuSans-91\"/>\n",
       "      <use transform=\"translate(414.716797 0.015625)\" xlink:href=\"#DejaVuSans-Oblique-107\"/>\n",
       "      <use transform=\"translate(472.626953 0.015625)\" xlink:href=\"#DejaVuSans-93\"/>\n",
       "      <use transform=\"translate(511.640625 0.015625)\" xlink:href=\"#DejaVuSans-44\"/>\n",
       "      <use transform=\"translate(543.427734 0.015625)\" xlink:href=\"#DejaVuSans-32\"/>\n",
       "      <use transform=\"translate(575.214844 0.015625)\" xlink:href=\"#DejaVuSans-Oblique-101\"/>\n",
       "      <use transform=\"translate(636.738281 0.015625)\" xlink:href=\"#DejaVuSans-91\"/>\n",
       "      <use transform=\"translate(675.751953 0.015625)\" xlink:href=\"#DejaVuSans-Oblique-107\"/>\n",
       "      <use transform=\"translate(733.662109 0.015625)\" xlink:href=\"#DejaVuSans-93\"/>\n",
       "     </g>\n",
       "    </g>\n",
       "   </g>\n",
       "   <g id=\"line2d_12\">\n",
       "    <path clip-path=\"url(#p84b8d34018)\" d=\"M 52.682813 118.08 \n",
       "L 71.755078 98.388606 \n",
       "L 82.108594 88.021329 \n",
       "L 90.827344 79.601909 \n",
       "L 98.45625 72.536207 \n",
       "L 105.540234 66.27487 \n",
       "L 112.079297 60.786714 \n",
       "L 118.073438 56.027953 \n",
       "L 124.067578 51.551768 \n",
       "L 129.516797 47.7449 \n",
       "L 134.966016 44.202756 \n",
       "L 140.415234 40.93867 \n",
       "L 145.319531 38.248908 \n",
       "L 150.223828 35.802538 \n",
       "L 155.128125 33.607019 \n",
       "L 160.032422 31.669044 \n",
       "L 164.936719 29.994522 \n",
       "L 169.296094 28.731374 \n",
       "L 173.655469 27.683475 \n",
       "L 178.014844 26.853349 \n",
       "L 182.374219 26.242996 \n",
       "L 186.733594 25.853886 \n",
       "L 191.092969 25.686958 \n",
       "L 195.452344 25.742612 \n",
       "L 199.811719 26.020715 \n",
       "L 204.171094 26.520596 \n",
       "L 208.530469 27.241053 \n",
       "L 212.889844 28.180348 \n",
       "L 217.249219 29.33622 \n",
       "L 221.608594 30.705883 \n",
       "L 225.967969 32.286038 \n",
       "L 230.872266 34.310557 \n",
       "L 235.776563 36.590475 \n",
       "L 240.680859 39.118842 \n",
       "L 245.585156 41.887948 \n",
       "L 251.034375 45.23679 \n",
       "L 256.483594 48.859797 \n",
       "L 261.932813 52.743333 \n",
       "L 267.926953 57.298662 \n",
       "L 273.921094 62.13078 \n",
       "L 280.460156 67.691971 \n",
       "L 287.544141 74.023751 \n",
       "L 295.173047 81.154724 \n",
       "L 303.891797 89.634693 \n",
       "L 313.700391 99.497932 \n",
       "L 327.323438 113.546147 \n",
       "L 351.844922 138.877753 \n",
       "L 362.198438 149.208622 \n",
       "L 370.917188 157.586091 \n",
       "L 378.546094 164.606947 \n",
       "L 385.630078 170.820141 \n",
       "L 392.169141 176.258573 \n",
       "L 398.163281 180.967532 \n",
       "L 404.157422 185.39011 \n",
       "L 409.606641 189.145148 \n",
       "L 415.055859 192.632714 \n",
       "L 420.505078 195.83968 \n",
       "L 425.409375 198.476038 \n",
       "L 430.313672 200.867281 \n",
       "L 435.217969 203.00612 \n",
       "L 440.122266 204.886032 \n",
       "L 444.481641 206.335044 \n",
       "L 448.841016 207.571442 \n",
       "L 453.200391 208.592246 \n",
       "L 457.559766 209.394999 \n",
       "L 461.919141 209.977766 \n",
       "L 466.278516 210.339144 \n",
       "L 470.637891 210.478261 \n",
       "L 474.997266 210.394782 \n",
       "L 479.356641 210.088909 \n",
       "L 483.716016 209.561379 \n",
       "L 488.075391 208.813462 \n",
       "L 492.434766 207.84696 \n",
       "L 496.794141 206.664201 \n",
       "L 501.153516 205.268036 \n",
       "L 506.057813 203.446469 \n",
       "L 510.962109 201.364633 \n",
       "L 515.866406 199.028877 \n",
       "L 520.770703 196.44632 \n",
       "L 525.675 193.624837 \n",
       "L 531.124219 190.22012 \n",
       "L 536.573437 186.543884 \n",
       "L 542.022656 182.609965 \n",
       "L 548.016797 178.002731 \n",
       "L 554.010937 173.122616 \n",
       "L 560.55 167.51378 \n",
       "L 567.633984 161.136228 \n",
       "L 575.262891 153.963082 \n",
       "L 583.981641 145.444342 \n",
       "L 594.335156 134.992886 \n",
       "L 609.048047 119.780782 \n",
       "L 610.137891 118.646956 \n",
       "L 610.137891 118.646956 \n",
       "\" style=\"fill:none;stroke:#ff0000;stroke-linecap:square;stroke-width:1.5;\"/>\n",
       "   </g>\n",
       "   <g id=\"line2d_13\">\n",
       "    <path clip-path=\"url(#p84b8d34018)\" d=\"M 52.682813 118.08 \n",
       "L 67.395703 118.08 \n",
       "L 67.940625 87.28 \n",
       "L 99.001172 87.28 \n",
       "L 99.546094 56.48 \n",
       "L 139.870313 56.48 \n",
       "L 140.415234 25.68 \n",
       "L 243.950391 25.68 \n",
       "L 244.495313 56.48 \n",
       "L 284.819531 56.48 \n",
       "L 285.364453 87.28 \n",
       "L 316.425 87.28 \n",
       "L 316.969922 118.08 \n",
       "L 346.395703 118.08 \n",
       "L 346.940625 148.88 \n",
       "L 378.001172 148.88 \n",
       "L 378.546094 179.68 \n",
       "L 418.870313 179.68 \n",
       "L 419.415234 210.48 \n",
       "L 522.950391 210.48 \n",
       "L 523.495312 179.68 \n",
       "L 563.819531 179.68 \n",
       "L 564.364453 148.88 \n",
       "L 595.425 148.88 \n",
       "L 595.969922 118.08 \n",
       "L 610.137891 118.08 \n",
       "L 610.137891 118.08 \n",
       "\" style=\"fill:none;stroke:#0000ff;stroke-linecap:square;stroke-width:1.5;\"/>\n",
       "   </g>\n",
       "   <g id=\"line2d_14\">\n",
       "    <path clip-path=\"url(#p84b8d34018)\" d=\"M 52.682813 118.08 \n",
       "L 67.395703 133.317972 \n",
       "L 67.940625 103.076879 \n",
       "L 79.383984 114.644342 \n",
       "L 88.102734 123.163082 \n",
       "L 96.276563 130.837058 \n",
       "L 99.001172 133.316236 \n",
       "L 99.546094 103.006947 \n",
       "L 106.630078 109.220141 \n",
       "L 113.169141 114.658573 \n",
       "L 119.163281 119.367532 \n",
       "L 125.157422 123.79011 \n",
       "L 130.606641 127.545148 \n",
       "L 136.055859 131.032714 \n",
       "L 139.870313 133.307792 \n",
       "L 140.415234 102.82133 \n",
       "L 145.319531 105.511092 \n",
       "L 150.223828 107.957462 \n",
       "L 155.128125 110.152981 \n",
       "L 160.032422 112.090956 \n",
       "L 164.936719 113.765478 \n",
       "L 169.296094 115.028626 \n",
       "L 173.655469 116.076525 \n",
       "L 178.014844 116.906651 \n",
       "L 182.374219 117.517004 \n",
       "L 186.733594 117.906114 \n",
       "L 191.092969 118.073042 \n",
       "L 195.452344 118.017388 \n",
       "L 199.811719 117.739285 \n",
       "L 204.171094 117.239404 \n",
       "L 208.530469 116.518947 \n",
       "L 212.889844 115.579652 \n",
       "L 217.249219 114.42378 \n",
       "L 221.608594 113.054117 \n",
       "L 225.967969 111.473962 \n",
       "L 230.872266 109.449443 \n",
       "L 235.776563 107.169525 \n",
       "L 240.680859 104.641158 \n",
       "L 243.950391 102.82133 \n",
       "L 244.495313 133.307792 \n",
       "L 249.944531 130.01533 \n",
       "L 255.39375 126.446097 \n",
       "L 260.842969 122.613528 \n",
       "L 266.837109 118.110793 \n",
       "L 272.83125 113.327399 \n",
       "L 279.370313 107.81469 \n",
       "L 284.819531 103.006947 \n",
       "L 285.364453 133.316236 \n",
       "L 292.993359 126.272825 \n",
       "L 301.167188 118.408622 \n",
       "L 310.430859 109.180981 \n",
       "L 316.425 103.076879 \n",
       "L 316.969922 133.317972 \n",
       "L 333.317578 116.379218 \n",
       "L 346.395703 102.842028 \n",
       "L 346.940625 133.083121 \n",
       "L 358.383984 121.515658 \n",
       "L 367.102734 112.996918 \n",
       "L 375.276563 105.322942 \n",
       "L 378.001172 102.843764 \n",
       "L 378.546094 133.153053 \n",
       "L 385.630078 126.939859 \n",
       "L 392.169141 121.501427 \n",
       "L 398.163281 116.792468 \n",
       "L 404.157422 112.36989 \n",
       "L 409.606641 108.614852 \n",
       "L 415.055859 105.127286 \n",
       "L 418.870313 102.852208 \n",
       "L 419.415234 133.33867 \n",
       "L 424.319531 130.648908 \n",
       "L 429.223828 128.202538 \n",
       "L 434.128125 126.007019 \n",
       "L 439.032422 124.069044 \n",
       "L 443.936719 122.394522 \n",
       "L 448.296094 121.131374 \n",
       "L 452.655469 120.083475 \n",
       "L 457.014844 119.253349 \n",
       "L 461.374219 118.642996 \n",
       "L 465.733594 118.253886 \n",
       "L 470.092969 118.086958 \n",
       "L 474.452344 118.142612 \n",
       "L 478.811719 118.420715 \n",
       "L 483.171094 118.920596 \n",
       "L 487.530469 119.641053 \n",
       "L 491.889844 120.580348 \n",
       "L 496.249219 121.73622 \n",
       "L 500.608594 123.105883 \n",
       "L 504.967969 124.686038 \n",
       "L 509.872266 126.710557 \n",
       "L 514.776562 128.990475 \n",
       "L 519.680859 131.518842 \n",
       "L 522.950391 133.33867 \n",
       "L 523.495312 102.852208 \n",
       "L 528.944531 106.14467 \n",
       "L 534.39375 109.713903 \n",
       "L 539.842969 113.546472 \n",
       "L 545.837109 118.049207 \n",
       "L 551.83125 122.832601 \n",
       "L 558.370312 128.34531 \n",
       "L 563.819531 133.153053 \n",
       "L 564.364453 102.843764 \n",
       "L 571.993359 109.887175 \n",
       "L 580.167187 117.751378 \n",
       "L 589.430859 126.979019 \n",
       "L 595.425 133.083121 \n",
       "L 595.969922 102.842028 \n",
       "L 610.137891 117.513044 \n",
       "L 610.137891 117.513044 \n",
       "\" style=\"fill:none;stroke:#008000;stroke-linecap:square;stroke-width:1.5;\"/>\n",
       "   </g>\n",
       "   <g id=\"patch_3\">\n",
       "    <path d=\"M 52.682813 228.96 \n",
       "L 52.682813 7.2 \n",
       "\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;stroke-width:0.8;\"/>\n",
       "   </g>\n",
       "   <g id=\"patch_4\">\n",
       "    <path d=\"M 610.682812 228.96 \n",
       "L 610.682812 7.2 \n",
       "\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;stroke-width:0.8;\"/>\n",
       "   </g>\n",
       "   <g id=\"patch_5\">\n",
       "    <path d=\"M 52.682813 228.96 \n",
       "L 610.682812 228.96 \n",
       "\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;stroke-width:0.8;\"/>\n",
       "   </g>\n",
       "   <g id=\"patch_6\">\n",
       "    <path d=\"M 52.682813 7.2 \n",
       "L 610.682812 7.2 \n",
       "\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;stroke-width:0.8;\"/>\n",
       "   </g>\n",
       "   <g id=\"legend_1\">\n",
       "    <g id=\"patch_7\">\n",
       "     <path d=\"M 458.582812 59.8 \n",
       "L 603.682812 59.8 \n",
       "Q 605.682812 59.8 605.682812 57.8 \n",
       "L 605.682812 14.2 \n",
       "Q 605.682812 12.2 603.682812 12.2 \n",
       "L 458.582812 12.2 \n",
       "Q 456.582812 12.2 456.582812 14.2 \n",
       "L 456.582812 57.8 \n",
       "Q 456.582812 59.8 458.582812 59.8 \n",
       "z\n",
       "\" style=\"fill:#ffffff;opacity:0.8;stroke:#cccccc;stroke-linejoin:miter;\"/>\n",
       "    </g>\n",
       "    <g id=\"line2d_15\">\n",
       "     <path d=\"M 460.582812 20.3 \n",
       "L 480.582812 20.3 \n",
       "\" style=\"fill:none;stroke:#ff0000;stroke-linecap:square;stroke-width:1.5;\"/>\n",
       "    </g>\n",
       "    <g id=\"line2d_16\"/>\n",
       "    <g id=\"text_14\">\n",
       "     <!-- signal $x[k]$ -->\n",
       "     <defs>\n",
       "      <path d=\"M 44.28125 53.078125 \n",
       "L 44.28125 44.578125 \n",
       "Q 40.484375 46.53125 36.375 47.5 \n",
       "Q 32.28125 48.484375 27.875 48.484375 \n",
       "Q 21.1875 48.484375 17.84375 46.4375 \n",
       "Q 14.5 44.390625 14.5 40.28125 \n",
       "Q 14.5 37.15625 16.890625 35.375 \n",
       "Q 19.28125 33.59375 26.515625 31.984375 \n",
       "L 29.59375 31.296875 \n",
       "Q 39.15625 29.25 43.1875 25.515625 \n",
       "Q 47.21875 21.78125 47.21875 15.09375 \n",
       "Q 47.21875 7.46875 41.1875 3.015625 \n",
       "Q 35.15625 -1.421875 24.609375 -1.421875 \n",
       "Q 20.21875 -1.421875 15.453125 -0.5625 \n",
       "Q 10.6875 0.296875 5.421875 2 \n",
       "L 5.421875 11.28125 \n",
       "Q 10.40625 8.6875 15.234375 7.390625 \n",
       "Q 20.0625 6.109375 24.8125 6.109375 \n",
       "Q 31.15625 6.109375 34.5625 8.28125 \n",
       "Q 37.984375 10.453125 37.984375 14.40625 \n",
       "Q 37.984375 18.0625 35.515625 20.015625 \n",
       "Q 33.0625 21.96875 24.703125 23.78125 \n",
       "L 21.578125 24.515625 \n",
       "Q 13.234375 26.265625 9.515625 29.90625 \n",
       "Q 5.8125 33.546875 5.8125 39.890625 \n",
       "Q 5.8125 47.609375 11.28125 51.796875 \n",
       "Q 16.75 56 26.8125 56 \n",
       "Q 31.78125 56 36.171875 55.265625 \n",
       "Q 40.578125 54.546875 44.28125 53.078125 \n",
       "z\n",
       "\" id=\"DejaVuSans-115\"/>\n",
       "      <path d=\"M 9.421875 54.6875 \n",
       "L 18.40625 54.6875 \n",
       "L 18.40625 0 \n",
       "L 9.421875 0 \n",
       "z\n",
       "M 9.421875 75.984375 \n",
       "L 18.40625 75.984375 \n",
       "L 18.40625 64.59375 \n",
       "L 9.421875 64.59375 \n",
       "z\n",
       "\" id=\"DejaVuSans-105\"/>\n",
       "      <path d=\"M 45.40625 27.984375 \n",
       "Q 45.40625 37.75 41.375 43.109375 \n",
       "Q 37.359375 48.484375 30.078125 48.484375 \n",
       "Q 22.859375 48.484375 18.828125 43.109375 \n",
       "Q 14.796875 37.75 14.796875 27.984375 \n",
       "Q 14.796875 18.265625 18.828125 12.890625 \n",
       "Q 22.859375 7.515625 30.078125 7.515625 \n",
       "Q 37.359375 7.515625 41.375 12.890625 \n",
       "Q 45.40625 18.265625 45.40625 27.984375 \n",
       "z\n",
       "M 54.390625 6.78125 \n",
       "Q 54.390625 -7.171875 48.1875 -13.984375 \n",
       "Q 42 -20.796875 29.203125 -20.796875 \n",
       "Q 24.46875 -20.796875 20.265625 -20.09375 \n",
       "Q 16.0625 -19.390625 12.109375 -17.921875 \n",
       "L 12.109375 -9.1875 \n",
       "Q 16.0625 -11.328125 19.921875 -12.34375 \n",
       "Q 23.78125 -13.375 27.78125 -13.375 \n",
       "Q 36.625 -13.375 41.015625 -8.765625 \n",
       "Q 45.40625 -4.15625 45.40625 5.171875 \n",
       "L 45.40625 9.625 \n",
       "Q 42.625 4.78125 38.28125 2.390625 \n",
       "Q 33.9375 0 27.875 0 \n",
       "Q 17.828125 0 11.671875 7.65625 \n",
       "Q 5.515625 15.328125 5.515625 27.984375 \n",
       "Q 5.515625 40.671875 11.671875 48.328125 \n",
       "Q 17.828125 56 27.875 56 \n",
       "Q 33.9375 56 38.28125 53.609375 \n",
       "Q 42.625 51.21875 45.40625 46.390625 \n",
       "L 45.40625 54.6875 \n",
       "L 54.390625 54.6875 \n",
       "z\n",
       "\" id=\"DejaVuSans-103\"/>\n",
       "      <path d=\"M 54.890625 33.015625 \n",
       "L 54.890625 0 \n",
       "L 45.90625 0 \n",
       "L 45.90625 32.71875 \n",
       "Q 45.90625 40.484375 42.875 44.328125 \n",
       "Q 39.84375 48.1875 33.796875 48.1875 \n",
       "Q 26.515625 48.1875 22.3125 43.546875 \n",
       "Q 18.109375 38.921875 18.109375 30.90625 \n",
       "L 18.109375 0 \n",
       "L 9.078125 0 \n",
       "L 9.078125 54.6875 \n",
       "L 18.109375 54.6875 \n",
       "L 18.109375 46.1875 \n",
       "Q 21.34375 51.125 25.703125 53.5625 \n",
       "Q 30.078125 56 35.796875 56 \n",
       "Q 45.21875 56 50.046875 50.171875 \n",
       "Q 54.890625 44.34375 54.890625 33.015625 \n",
       "z\n",
       "\" id=\"DejaVuSans-110\"/>\n",
       "      <path d=\"M 34.28125 27.484375 \n",
       "Q 23.390625 27.484375 19.1875 25 \n",
       "Q 14.984375 22.515625 14.984375 16.5 \n",
       "Q 14.984375 11.71875 18.140625 8.90625 \n",
       "Q 21.296875 6.109375 26.703125 6.109375 \n",
       "Q 34.1875 6.109375 38.703125 11.40625 \n",
       "Q 43.21875 16.703125 43.21875 25.484375 \n",
       "L 43.21875 27.484375 \n",
       "z\n",
       "M 52.203125 31.203125 \n",
       "L 52.203125 0 \n",
       "L 43.21875 0 \n",
       "L 43.21875 8.296875 \n",
       "Q 40.140625 3.328125 35.546875 0.953125 \n",
       "Q 30.953125 -1.421875 24.3125 -1.421875 \n",
       "Q 15.921875 -1.421875 10.953125 3.296875 \n",
       "Q 6 8.015625 6 15.921875 \n",
       "Q 6 25.140625 12.171875 29.828125 \n",
       "Q 18.359375 34.515625 30.609375 34.515625 \n",
       "L 43.21875 34.515625 \n",
       "L 43.21875 35.40625 \n",
       "Q 43.21875 41.609375 39.140625 45 \n",
       "Q 35.0625 48.390625 27.6875 48.390625 \n",
       "Q 23 48.390625 18.546875 47.265625 \n",
       "Q 14.109375 46.140625 10.015625 43.890625 \n",
       "L 10.015625 52.203125 \n",
       "Q 14.9375 54.109375 19.578125 55.046875 \n",
       "Q 24.21875 56 28.609375 56 \n",
       "Q 40.484375 56 46.34375 49.84375 \n",
       "Q 52.203125 43.703125 52.203125 31.203125 \n",
       "z\n",
       "\" id=\"DejaVuSans-97\"/>\n",
       "      <path d=\"M 9.421875 75.984375 \n",
       "L 18.40625 75.984375 \n",
       "L 18.40625 0 \n",
       "L 9.421875 0 \n",
       "z\n",
       "\" id=\"DejaVuSans-108\"/>\n",
       "     </defs>\n",
       "     <g transform=\"translate(488.582812 23.8)scale(0.1 -0.1)\">\n",
       "      <use transform=\"translate(0 0.015625)\" xlink:href=\"#DejaVuSans-115\"/>\n",
       "      <use transform=\"translate(52.099609 0.015625)\" xlink:href=\"#DejaVuSans-105\"/>\n",
       "      <use transform=\"translate(79.882812 0.015625)\" xlink:href=\"#DejaVuSans-103\"/>\n",
       "      <use transform=\"translate(143.359375 0.015625)\" xlink:href=\"#DejaVuSans-110\"/>\n",
       "      <use transform=\"translate(206.738281 0.015625)\" xlink:href=\"#DejaVuSans-97\"/>\n",
       "      <use transform=\"translate(268.017578 0.015625)\" xlink:href=\"#DejaVuSans-108\"/>\n",
       "      <use transform=\"translate(295.800781 0.015625)\" xlink:href=\"#DejaVuSans-32\"/>\n",
       "      <use transform=\"translate(327.587891 0.015625)\" xlink:href=\"#DejaVuSans-Oblique-120\"/>\n",
       "      <use transform=\"translate(386.767578 0.015625)\" xlink:href=\"#DejaVuSans-91\"/>\n",
       "      <use transform=\"translate(425.78125 0.015625)\" xlink:href=\"#DejaVuSans-Oblique-107\"/>\n",
       "      <use transform=\"translate(483.691406 0.015625)\" xlink:href=\"#DejaVuSans-93\"/>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"line2d_17\">\n",
       "     <path d=\"M 460.582812 35 \n",
       "L 480.582812 35 \n",
       "\" style=\"fill:none;stroke:#0000ff;stroke-linecap:square;stroke-width:1.5;\"/>\n",
       "    </g>\n",
       "    <g id=\"line2d_18\"/>\n",
       "    <g id=\"text_15\">\n",
       "     <!-- quantized signal $x_Q[k]$ -->\n",
       "     <defs>\n",
       "      <path d=\"M 14.796875 27.296875 \n",
       "Q 14.796875 17.390625 18.875 11.75 \n",
       "Q 22.953125 6.109375 30.078125 6.109375 \n",
       "Q 37.203125 6.109375 41.296875 11.75 \n",
       "Q 45.40625 17.390625 45.40625 27.296875 \n",
       "Q 45.40625 37.203125 41.296875 42.84375 \n",
       "Q 37.203125 48.484375 30.078125 48.484375 \n",
       "Q 22.953125 48.484375 18.875 42.84375 \n",
       "Q 14.796875 37.203125 14.796875 27.296875 \n",
       "z\n",
       "M 45.40625 8.203125 \n",
       "Q 42.578125 3.328125 38.25 0.953125 \n",
       "Q 33.9375 -1.421875 27.875 -1.421875 \n",
       "Q 17.96875 -1.421875 11.734375 6.484375 \n",
       "Q 5.515625 14.40625 5.515625 27.296875 \n",
       "Q 5.515625 40.1875 11.734375 48.09375 \n",
       "Q 17.96875 56 27.875 56 \n",
       "Q 33.9375 56 38.25 53.625 \n",
       "Q 42.578125 51.265625 45.40625 46.390625 \n",
       "L 45.40625 54.6875 \n",
       "L 54.390625 54.6875 \n",
       "L 54.390625 -20.796875 \n",
       "L 45.40625 -20.796875 \n",
       "z\n",
       "\" id=\"DejaVuSans-113\"/>\n",
       "      <path d=\"M 8.5 21.578125 \n",
       "L 8.5 54.6875 \n",
       "L 17.484375 54.6875 \n",
       "L 17.484375 21.921875 \n",
       "Q 17.484375 14.15625 20.5 10.265625 \n",
       "Q 23.53125 6.390625 29.59375 6.390625 \n",
       "Q 36.859375 6.390625 41.078125 11.03125 \n",
       "Q 45.3125 15.671875 45.3125 23.6875 \n",
       "L 45.3125 54.6875 \n",
       "L 54.296875 54.6875 \n",
       "L 54.296875 0 \n",
       "L 45.3125 0 \n",
       "L 45.3125 8.40625 \n",
       "Q 42.046875 3.421875 37.71875 1 \n",
       "Q 33.40625 -1.421875 27.6875 -1.421875 \n",
       "Q 18.265625 -1.421875 13.375 4.4375 \n",
       "Q 8.5 10.296875 8.5 21.578125 \n",
       "z\n",
       "M 31.109375 56 \n",
       "z\n",
       "\" id=\"DejaVuSans-117\"/>\n",
       "      <path d=\"M 18.3125 70.21875 \n",
       "L 18.3125 54.6875 \n",
       "L 36.8125 54.6875 \n",
       "L 36.8125 47.703125 \n",
       "L 18.3125 47.703125 \n",
       "L 18.3125 18.015625 \n",
       "Q 18.3125 11.328125 20.140625 9.421875 \n",
       "Q 21.96875 7.515625 27.59375 7.515625 \n",
       "L 36.8125 7.515625 \n",
       "L 36.8125 0 \n",
       "L 27.59375 0 \n",
       "Q 17.1875 0 13.234375 3.875 \n",
       "Q 9.28125 7.765625 9.28125 18.015625 \n",
       "L 9.28125 47.703125 \n",
       "L 2.6875 47.703125 \n",
       "L 2.6875 54.6875 \n",
       "L 9.28125 54.6875 \n",
       "L 9.28125 70.21875 \n",
       "z\n",
       "\" id=\"DejaVuSans-116\"/>\n",
       "      <path d=\"M 5.515625 54.6875 \n",
       "L 48.1875 54.6875 \n",
       "L 48.1875 46.484375 \n",
       "L 14.40625 7.171875 \n",
       "L 48.1875 7.171875 \n",
       "L 48.1875 0 \n",
       "L 4.296875 0 \n",
       "L 4.296875 8.203125 \n",
       "L 38.09375 47.515625 \n",
       "L 5.515625 47.515625 \n",
       "z\n",
       "\" id=\"DejaVuSans-122\"/>\n",
       "      <path d=\"M 56.203125 29.59375 \n",
       "L 56.203125 25.203125 \n",
       "L 14.890625 25.203125 \n",
       "Q 15.484375 15.921875 20.484375 11.0625 \n",
       "Q 25.484375 6.203125 34.421875 6.203125 \n",
       "Q 39.59375 6.203125 44.453125 7.46875 \n",
       "Q 49.3125 8.734375 54.109375 11.28125 \n",
       "L 54.109375 2.78125 \n",
       "Q 49.265625 0.734375 44.1875 -0.34375 \n",
       "Q 39.109375 -1.421875 33.890625 -1.421875 \n",
       "Q 20.796875 -1.421875 13.15625 6.1875 \n",
       "Q 5.515625 13.8125 5.515625 26.8125 \n",
       "Q 5.515625 40.234375 12.765625 48.109375 \n",
       "Q 20.015625 56 32.328125 56 \n",
       "Q 43.359375 56 49.78125 48.890625 \n",
       "Q 56.203125 41.796875 56.203125 29.59375 \n",
       "z\n",
       "M 47.21875 32.234375 \n",
       "Q 47.125 39.59375 43.09375 43.984375 \n",
       "Q 39.0625 48.390625 32.421875 48.390625 \n",
       "Q 24.90625 48.390625 20.390625 44.140625 \n",
       "Q 15.875 39.890625 15.1875 32.171875 \n",
       "z\n",
       "\" id=\"DejaVuSans-101\"/>\n",
       "      <path d=\"M 45.40625 46.390625 \n",
       "L 45.40625 75.984375 \n",
       "L 54.390625 75.984375 \n",
       "L 54.390625 0 \n",
       "L 45.40625 0 \n",
       "L 45.40625 8.203125 \n",
       "Q 42.578125 3.328125 38.25 0.953125 \n",
       "Q 33.9375 -1.421875 27.875 -1.421875 \n",
       "Q 17.96875 -1.421875 11.734375 6.484375 \n",
       "Q 5.515625 14.40625 5.515625 27.296875 \n",
       "Q 5.515625 40.1875 11.734375 48.09375 \n",
       "Q 17.96875 56 27.875 56 \n",
       "Q 33.9375 56 38.25 53.625 \n",
       "Q 42.578125 51.265625 45.40625 46.390625 \n",
       "z\n",
       "M 14.796875 27.296875 \n",
       "Q 14.796875 17.390625 18.875 11.75 \n",
       "Q 22.953125 6.109375 30.078125 6.109375 \n",
       "Q 37.203125 6.109375 41.296875 11.75 \n",
       "Q 45.40625 17.390625 45.40625 27.296875 \n",
       "Q 45.40625 37.203125 41.296875 42.84375 \n",
       "Q 37.203125 48.484375 30.078125 48.484375 \n",
       "Q 22.953125 48.484375 18.875 42.84375 \n",
       "Q 14.796875 37.203125 14.796875 27.296875 \n",
       "z\n",
       "\" id=\"DejaVuSans-100\"/>\n",
       "     </defs>\n",
       "     <g transform=\"translate(488.582812 38.5)scale(0.1 -0.1)\">\n",
       "      <use transform=\"translate(0 0.015625)\" xlink:href=\"#DejaVuSans-113\"/>\n",
       "      <use transform=\"translate(63.476562 0.015625)\" xlink:href=\"#DejaVuSans-117\"/>\n",
       "      <use transform=\"translate(126.855469 0.015625)\" xlink:href=\"#DejaVuSans-97\"/>\n",
       "      <use transform=\"translate(188.134766 0.015625)\" xlink:href=\"#DejaVuSans-110\"/>\n",
       "      <use transform=\"translate(251.513672 0.015625)\" xlink:href=\"#DejaVuSans-116\"/>\n",
       "      <use transform=\"translate(290.722656 0.015625)\" xlink:href=\"#DejaVuSans-105\"/>\n",
       "      <use transform=\"translate(318.505859 0.015625)\" xlink:href=\"#DejaVuSans-122\"/>\n",
       "      <use transform=\"translate(370.996094 0.015625)\" xlink:href=\"#DejaVuSans-101\"/>\n",
       "      <use transform=\"translate(432.519531 0.015625)\" xlink:href=\"#DejaVuSans-100\"/>\n",
       "      <use transform=\"translate(495.996094 0.015625)\" xlink:href=\"#DejaVuSans-32\"/>\n",
       "      <use transform=\"translate(527.783203 0.015625)\" xlink:href=\"#DejaVuSans-115\"/>\n",
       "      <use transform=\"translate(579.882812 0.015625)\" xlink:href=\"#DejaVuSans-105\"/>\n",
       "      <use transform=\"translate(607.666016 0.015625)\" xlink:href=\"#DejaVuSans-103\"/>\n",
       "      <use transform=\"translate(671.142578 0.015625)\" xlink:href=\"#DejaVuSans-110\"/>\n",
       "      <use transform=\"translate(734.521484 0.015625)\" xlink:href=\"#DejaVuSans-97\"/>\n",
       "      <use transform=\"translate(795.800781 0.015625)\" xlink:href=\"#DejaVuSans-108\"/>\n",
       "      <use transform=\"translate(823.583984 0.015625)\" xlink:href=\"#DejaVuSans-32\"/>\n",
       "      <use transform=\"translate(855.371094 0.015625)\" xlink:href=\"#DejaVuSans-Oblique-120\"/>\n",
       "      <use transform=\"translate(914.550781 -16.390625)scale(0.7)\" xlink:href=\"#DejaVuSans-Oblique-81\"/>\n",
       "      <use transform=\"translate(972.382812 0.015625)\" xlink:href=\"#DejaVuSans-91\"/>\n",
       "      <use transform=\"translate(1011.396484 0.015625)\" xlink:href=\"#DejaVuSans-Oblique-107\"/>\n",
       "      <use transform=\"translate(1069.306641 0.015625)\" xlink:href=\"#DejaVuSans-93\"/>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"line2d_19\">\n",
       "     <path d=\"M 460.582812 50.2 \n",
       "L 480.582812 50.2 \n",
       "\" style=\"fill:none;stroke:#008000;stroke-linecap:square;stroke-width:1.5;\"/>\n",
       "    </g>\n",
       "    <g id=\"line2d_20\"/>\n",
       "    <g id=\"text_16\">\n",
       "     <!-- quantization error $e[k]$ -->\n",
       "     <defs>\n",
       "      <path d=\"M 30.609375 48.390625 \n",
       "Q 23.390625 48.390625 19.1875 42.75 \n",
       "Q 14.984375 37.109375 14.984375 27.296875 \n",
       "Q 14.984375 17.484375 19.15625 11.84375 \n",
       "Q 23.34375 6.203125 30.609375 6.203125 \n",
       "Q 37.796875 6.203125 41.984375 11.859375 \n",
       "Q 46.1875 17.53125 46.1875 27.296875 \n",
       "Q 46.1875 37.015625 41.984375 42.703125 \n",
       "Q 37.796875 48.390625 30.609375 48.390625 \n",
       "z\n",
       "M 30.609375 56 \n",
       "Q 42.328125 56 49.015625 48.375 \n",
       "Q 55.71875 40.765625 55.71875 27.296875 \n",
       "Q 55.71875 13.875 49.015625 6.21875 \n",
       "Q 42.328125 -1.421875 30.609375 -1.421875 \n",
       "Q 18.84375 -1.421875 12.171875 6.21875 \n",
       "Q 5.515625 13.875 5.515625 27.296875 \n",
       "Q 5.515625 40.765625 12.171875 48.375 \n",
       "Q 18.84375 56 30.609375 56 \n",
       "z\n",
       "\" id=\"DejaVuSans-111\"/>\n",
       "      <path d=\"M 41.109375 46.296875 \n",
       "Q 39.59375 47.171875 37.8125 47.578125 \n",
       "Q 36.03125 48 33.890625 48 \n",
       "Q 26.265625 48 22.1875 43.046875 \n",
       "Q 18.109375 38.09375 18.109375 28.8125 \n",
       "L 18.109375 0 \n",
       "L 9.078125 0 \n",
       "L 9.078125 54.6875 \n",
       "L 18.109375 54.6875 \n",
       "L 18.109375 46.1875 \n",
       "Q 20.953125 51.171875 25.484375 53.578125 \n",
       "Q 30.03125 56 36.53125 56 \n",
       "Q 37.453125 56 38.578125 55.875 \n",
       "Q 39.703125 55.765625 41.0625 55.515625 \n",
       "z\n",
       "\" id=\"DejaVuSans-114\"/>\n",
       "     </defs>\n",
       "     <g transform=\"translate(488.582812 53.7)scale(0.1 -0.1)\">\n",
       "      <use transform=\"translate(0 0.015625)\" xlink:href=\"#DejaVuSans-113\"/>\n",
       "      <use transform=\"translate(63.476562 0.015625)\" xlink:href=\"#DejaVuSans-117\"/>\n",
       "      <use transform=\"translate(126.855469 0.015625)\" xlink:href=\"#DejaVuSans-97\"/>\n",
       "      <use transform=\"translate(188.134766 0.015625)\" xlink:href=\"#DejaVuSans-110\"/>\n",
       "      <use transform=\"translate(251.513672 0.015625)\" xlink:href=\"#DejaVuSans-116\"/>\n",
       "      <use transform=\"translate(290.722656 0.015625)\" xlink:href=\"#DejaVuSans-105\"/>\n",
       "      <use transform=\"translate(318.505859 0.015625)\" xlink:href=\"#DejaVuSans-122\"/>\n",
       "      <use transform=\"translate(370.996094 0.015625)\" xlink:href=\"#DejaVuSans-97\"/>\n",
       "      <use transform=\"translate(432.275391 0.015625)\" xlink:href=\"#DejaVuSans-116\"/>\n",
       "      <use transform=\"translate(471.484375 0.015625)\" xlink:href=\"#DejaVuSans-105\"/>\n",
       "      <use transform=\"translate(499.267578 0.015625)\" xlink:href=\"#DejaVuSans-111\"/>\n",
       "      <use transform=\"translate(560.449219 0.015625)\" xlink:href=\"#DejaVuSans-110\"/>\n",
       "      <use transform=\"translate(623.828125 0.015625)\" xlink:href=\"#DejaVuSans-32\"/>\n",
       "      <use transform=\"translate(655.615234 0.015625)\" xlink:href=\"#DejaVuSans-101\"/>\n",
       "      <use transform=\"translate(717.138672 0.015625)\" xlink:href=\"#DejaVuSans-114\"/>\n",
       "      <use transform=\"translate(758.251953 0.015625)\" xlink:href=\"#DejaVuSans-114\"/>\n",
       "      <use transform=\"translate(799.365234 0.015625)\" xlink:href=\"#DejaVuSans-111\"/>\n",
       "      <use transform=\"translate(860.546875 0.015625)\" xlink:href=\"#DejaVuSans-114\"/>\n",
       "      <use transform=\"translate(901.660156 0.015625)\" xlink:href=\"#DejaVuSans-32\"/>\n",
       "      <use transform=\"translate(933.447266 0.015625)\" xlink:href=\"#DejaVuSans-Oblique-101\"/>\n",
       "      <use transform=\"translate(994.970703 0.015625)\" xlink:href=\"#DejaVuSans-91\"/>\n",
       "      <use transform=\"translate(1033.984375 0.015625)\" xlink:href=\"#DejaVuSans-Oblique-107\"/>\n",
       "      <use transform=\"translate(1091.894531 0.015625)\" xlink:href=\"#DejaVuSans-93\"/>\n",
       "     </g>\n",
       "    </g>\n",
       "   </g>\n",
       "  </g>\n",
       "  <g id=\"axes_2\">\n",
       "   <g id=\"matplotlib.axis_3\">\n",
       "    <g id=\"ytick_6\">\n",
       "     <g id=\"line2d_21\">\n",
       "      <path clip-path=\"url(#p84b8d34018)\" d=\"M 52.682813 210.48 \n",
       "L 610.682812 210.48 \n",
       "\" style=\"fill:none;stroke:#b0b0b0;stroke-linecap:square;stroke-width:0.8;\"/>\n",
       "     </g>\n",
       "     <g id=\"line2d_22\">\n",
       "      <defs>\n",
       "       <path d=\"M 0 0 \n",
       "L 3.5 0 \n",
       "\" id=\"m4e1bbeb546\" style=\"stroke:#000000;stroke-width:0.8;\"/>\n",
       "      </defs>\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"610.682812\" xlink:href=\"#m4e1bbeb546\" y=\"210.48\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_17\">\n",
       "      <!-- −3 -->\n",
       "      <defs>\n",
       "       <path d=\"M 40.578125 39.3125 \n",
       "Q 47.65625 37.796875 51.625 33 \n",
       "Q 55.609375 28.21875 55.609375 21.1875 \n",
       "Q 55.609375 10.40625 48.1875 4.484375 \n",
       "Q 40.765625 -1.421875 27.09375 -1.421875 \n",
       "Q 22.515625 -1.421875 17.65625 -0.515625 \n",
       "Q 12.796875 0.390625 7.625 2.203125 \n",
       "L 7.625 11.71875 \n",
       "Q 11.71875 9.328125 16.59375 8.109375 \n",
       "Q 21.484375 6.890625 26.8125 6.890625 \n",
       "Q 36.078125 6.890625 40.9375 10.546875 \n",
       "Q 45.796875 14.203125 45.796875 21.1875 \n",
       "Q 45.796875 27.640625 41.28125 31.265625 \n",
       "Q 36.765625 34.90625 28.71875 34.90625 \n",
       "L 20.21875 34.90625 \n",
       "L 20.21875 43.015625 \n",
       "L 29.109375 43.015625 \n",
       "Q 36.375 43.015625 40.234375 45.921875 \n",
       "Q 44.09375 48.828125 44.09375 54.296875 \n",
       "Q 44.09375 59.90625 40.109375 62.90625 \n",
       "Q 36.140625 65.921875 28.71875 65.921875 \n",
       "Q 24.65625 65.921875 20.015625 65.03125 \n",
       "Q 15.375 64.15625 9.8125 62.3125 \n",
       "L 9.8125 71.09375 \n",
       "Q 15.4375 72.65625 20.34375 73.4375 \n",
       "Q 25.25 74.21875 29.59375 74.21875 \n",
       "Q 40.828125 74.21875 47.359375 69.109375 \n",
       "Q 53.90625 64.015625 53.90625 55.328125 \n",
       "Q 53.90625 49.265625 50.4375 45.09375 \n",
       "Q 46.96875 40.921875 40.578125 39.3125 \n",
       "z\n",
       "\" id=\"DejaVuSans-51\"/>\n",
       "      </defs>\n",
       "      <g transform=\"translate(617.682812 214.279219)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-8722\"/>\n",
       "       <use x=\"83.789062\" xlink:href=\"#DejaVuSans-51\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"ytick_7\">\n",
       "     <g id=\"line2d_23\">\n",
       "      <path clip-path=\"url(#p84b8d34018)\" d=\"M 52.682813 179.68 \n",
       "L 610.682812 179.68 \n",
       "\" style=\"fill:none;stroke:#b0b0b0;stroke-linecap:square;stroke-width:0.8;\"/>\n",
       "     </g>\n",
       "     <g id=\"line2d_24\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"610.682812\" xlink:href=\"#m4e1bbeb546\" y=\"179.68\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_18\">\n",
       "      <!-- −2 -->\n",
       "      <g transform=\"translate(617.682812 183.479219)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-8722\"/>\n",
       "       <use x=\"83.789062\" xlink:href=\"#DejaVuSans-50\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"ytick_8\">\n",
       "     <g id=\"line2d_25\">\n",
       "      <path clip-path=\"url(#p84b8d34018)\" d=\"M 52.682813 148.88 \n",
       "L 610.682812 148.88 \n",
       "\" style=\"fill:none;stroke:#b0b0b0;stroke-linecap:square;stroke-width:0.8;\"/>\n",
       "     </g>\n",
       "     <g id=\"line2d_26\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"610.682812\" xlink:href=\"#m4e1bbeb546\" y=\"148.88\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_19\">\n",
       "      <!-- −1 -->\n",
       "      <g transform=\"translate(617.682812 152.679219)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-8722\"/>\n",
       "       <use x=\"83.789062\" xlink:href=\"#DejaVuSans-49\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"ytick_9\">\n",
       "     <g id=\"line2d_27\">\n",
       "      <path clip-path=\"url(#p84b8d34018)\" d=\"M 52.682813 118.08 \n",
       "L 610.682812 118.08 \n",
       "\" style=\"fill:none;stroke:#b0b0b0;stroke-linecap:square;stroke-width:0.8;\"/>\n",
       "     </g>\n",
       "     <g id=\"line2d_28\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"610.682812\" xlink:href=\"#m4e1bbeb546\" y=\"118.08\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_20\">\n",
       "      <!-- 0 -->\n",
       "      <g transform=\"translate(617.682812 121.879219)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-48\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"ytick_10\">\n",
       "     <g id=\"line2d_29\">\n",
       "      <path clip-path=\"url(#p84b8d34018)\" d=\"M 52.682813 87.28 \n",
       "L 610.682812 87.28 \n",
       "\" style=\"fill:none;stroke:#b0b0b0;stroke-linecap:square;stroke-width:0.8;\"/>\n",
       "     </g>\n",
       "     <g id=\"line2d_30\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"610.682812\" xlink:href=\"#m4e1bbeb546\" y=\"87.28\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_21\">\n",
       "      <!-- 1 -->\n",
       "      <g transform=\"translate(617.682812 91.079219)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-49\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"ytick_11\">\n",
       "     <g id=\"line2d_31\">\n",
       "      <path clip-path=\"url(#p84b8d34018)\" d=\"M 52.682813 56.48 \n",
       "L 610.682812 56.48 \n",
       "\" style=\"fill:none;stroke:#b0b0b0;stroke-linecap:square;stroke-width:0.8;\"/>\n",
       "     </g>\n",
       "     <g id=\"line2d_32\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"610.682812\" xlink:href=\"#m4e1bbeb546\" y=\"56.48\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_22\">\n",
       "      <!-- 2 -->\n",
       "      <g transform=\"translate(617.682812 60.279219)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-50\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"ytick_12\">\n",
       "     <g id=\"line2d_33\">\n",
       "      <path clip-path=\"url(#p84b8d34018)\" d=\"M 52.682813 25.68 \n",
       "L 610.682812 25.68 \n",
       "\" style=\"fill:none;stroke:#b0b0b0;stroke-linecap:square;stroke-width:0.8;\"/>\n",
       "     </g>\n",
       "     <g id=\"line2d_34\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"610.682812\" xlink:href=\"#m4e1bbeb546\" y=\"25.68\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_23\">\n",
       "      <!-- 3 -->\n",
       "      <g transform=\"translate(617.682812 29.479219)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-51\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"text_24\">\n",
       "     <!-- quantization index -->\n",
       "     <defs>\n",
       "      <path d=\"M 54.890625 54.6875 \n",
       "L 35.109375 28.078125 \n",
       "L 55.90625 0 \n",
       "L 45.3125 0 \n",
       "L 29.390625 21.484375 \n",
       "L 13.484375 0 \n",
       "L 2.875 0 \n",
       "L 24.125 28.609375 \n",
       "L 4.6875 54.6875 \n",
       "L 15.28125 54.6875 \n",
       "L 29.78125 35.203125 \n",
       "L 44.28125 54.6875 \n",
       "z\n",
       "\" id=\"DejaVuSans-120\"/>\n",
       "     </defs>\n",
       "     <g transform=\"translate(644.023438 164.626875)rotate(-90)scale(0.1 -0.1)\">\n",
       "      <use xlink:href=\"#DejaVuSans-113\"/>\n",
       "      <use x=\"63.476562\" xlink:href=\"#DejaVuSans-117\"/>\n",
       "      <use x=\"126.855469\" xlink:href=\"#DejaVuSans-97\"/>\n",
       "      <use x=\"188.134766\" xlink:href=\"#DejaVuSans-110\"/>\n",
       "      <use x=\"251.513672\" xlink:href=\"#DejaVuSans-116\"/>\n",
       "      <use x=\"290.722656\" xlink:href=\"#DejaVuSans-105\"/>\n",
       "      <use x=\"318.505859\" xlink:href=\"#DejaVuSans-122\"/>\n",
       "      <use x=\"370.996094\" xlink:href=\"#DejaVuSans-97\"/>\n",
       "      <use x=\"432.275391\" xlink:href=\"#DejaVuSans-116\"/>\n",
       "      <use x=\"471.484375\" xlink:href=\"#DejaVuSans-105\"/>\n",
       "      <use x=\"499.267578\" xlink:href=\"#DejaVuSans-111\"/>\n",
       "      <use x=\"560.449219\" xlink:href=\"#DejaVuSans-110\"/>\n",
       "      <use x=\"623.828125\" xlink:href=\"#DejaVuSans-32\"/>\n",
       "      <use x=\"655.615234\" xlink:href=\"#DejaVuSans-105\"/>\n",
       "      <use x=\"683.398438\" xlink:href=\"#DejaVuSans-110\"/>\n",
       "      <use x=\"746.777344\" xlink:href=\"#DejaVuSans-100\"/>\n",
       "      <use x=\"810.253906\" xlink:href=\"#DejaVuSans-101\"/>\n",
       "      <use x=\"871.761719\" xlink:href=\"#DejaVuSans-120\"/>\n",
       "     </g>\n",
       "    </g>\n",
       "   </g>\n",
       "   <g id=\"patch_8\">\n",
       "    <path d=\"M 52.682813 228.96 \n",
       "L 52.682813 7.2 \n",
       "\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;stroke-width:0.8;\"/>\n",
       "   </g>\n",
       "   <g id=\"patch_9\">\n",
       "    <path d=\"M 610.682812 228.96 \n",
       "L 610.682812 7.2 \n",
       "\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;stroke-width:0.8;\"/>\n",
       "   </g>\n",
       "   <g id=\"patch_10\">\n",
       "    <path d=\"M 52.682813 228.96 \n",
       "L 610.682812 228.96 \n",
       "\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;stroke-width:0.8;\"/>\n",
       "   </g>\n",
       "   <g id=\"patch_11\">\n",
       "    <path d=\"M 52.682813 7.2 \n",
       "L 610.682812 7.2 \n",
       "\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;stroke-width:0.8;\"/>\n",
       "   </g>\n",
       "  </g>\n",
       " </g>\n",
       " <defs>\n",
       "  <clipPath id=\"p84b8d34018\">\n",
       "   <rect height=\"221.76\" width=\"558\" x=\"52.682813\" y=\"7.2\"/>\n",
       "  </clipPath>\n",
       " </defs>\n",
       "</svg>\n"
      ],
      "text/plain": [
       "<Figure size 960x384 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "\n",
    "N = 1024  # length of signal\n",
    "\n",
    "# generate signal\n",
    "x = np.sin(2*np.pi/N * np.arange(N))\n",
    "# quantize signal\n",
    "xi = np.round(3 * x)\n",
    "xQ = 1/3 * xi\n",
    "e = xQ - x\n",
    "\n",
    "# plot (quantized) signals\n",
    "fig, ax1 = plt.subplots(figsize=(10, 4))\n",
    "ax2 = ax1.twinx()\n",
    "\n",
    "ax1.plot(x, 'r', label=r'signal $x[k]$')\n",
    "ax1.plot(xQ, 'b', label=r'quantized signal $x_Q[k]$')\n",
    "ax1.plot(e, 'g', label=r'quantization error $e[k]$')\n",
    "ax1.set_xlabel('k')\n",
    "ax1.set_ylabel(r'$x[k]$, $x_Q[k]$, $e[k]$')\n",
    "ax1.axis([0, N, -1.2, 1.2])\n",
    "ax1.legend()\n",
    "\n",
    "ax2.set_ylim([-3.6, 3.6])\n",
    "ax2.set_ylabel('quantization index')\n",
    "ax2.grid()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Exercise**\n",
    "\n",
    "* Investigate the quantization error $e[k]$. Is its amplitude bounded?\n",
    "* If you would represent the quantization index (shown on the right side) by a binary number, how much bits would you need?\n",
    "* Try out other rounding operations like `np.floor()` and `np.ceil()` instead of `np.round()`. What changes?\n",
    "\n",
    "Solution: It can be concluded from the illustration that the quantization error is bounded as $|e[k]| < \\frac{1}{3}$. There are in total 7 quantization indexes needing 3 bits in a binary representation. The properties of the quantization error are different for different rounding operations."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Properties\n",
    "\n",
    "Without knowledge of the quantization error $e[k]$, the signal $x[k]$ cannot be reconstructed exactly from its quantization index or quantized representation $x_Q[k]$. The quantization error $e[k]$ itself depends on the signal $x[k]$. Therefore, quantization is in general an irreversible process. The mapping from $x[k]$ to $x_Q[k]$ is furthermore non-linear, since the superposition principle does not hold in general. Summarizing, quantization is an inherently irreversible and non-linear process. It potentially removes information from the signal."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Applications\n",
    "\n",
    "Quantization has widespread applications in Digital Signal Processing. For instance\n",
    "\n",
    "* [Analog-to-Digital conversion](https://en.wikipedia.org/wiki/Analog-to-digital_converter)\n",
    "* [Lossy compression](https://en.wikipedia.org/wiki/Lossy_compression) of signals (speech, music, video, ...)\n",
    "* Storage and transmission ([Pulse-Code Modulation](https://en.wikipedia.org/wiki/Pulse-code_modulation), ...)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "nbsphinx": "hidden"
   },
   "source": [
    "**Copyright**\n",
    "\n",
    "This notebook is provided as [Open Educational Resource](https://en.wikipedia.org/wiki/Open_educational_resources). Feel free to use the notebook for your own purposes. The text is licensed under [Creative Commons Attribution 4.0](https://creativecommons.org/licenses/by/4.0/), the code of the IPython examples under the [MIT license](https://opensource.org/licenses/MIT). Please attribute the work as follows: *Sascha Spors, Digital Signal Processing - Lecture notes featuring computational examples*."
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.5"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}
